A limiting process in the solution of an optimal control problem

Applications of Functional Analysis to the Theory of Optimal Processes

“…In [17] the author established, for an optimal high-speed problem, existence of an optimal Lyapunov function (optimal time 7'(x0, t) which has continuous partial derivatives of any order in x0 and the parameter This fact made it possible to prove [31] that the function T T(x0, t), subject to the restrictions (5), has continuous partial derivatives of ay order in the coordinates x0, x0 0, and the parameter at any point which is not a control switching point.…”